In the mobile telephone model, pairwise, broadcast, and all-to-all capacities are characterized to within constants, and one-shot gossip is solved within polylog factors in every graph.
On a connection between the existence of k-trees and the toughness of a graph
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The Capacity of Smartphone Peer-to-Peer Networks
In the mobile telephone model, pairwise, broadcast, and all-to-all capacities are characterized to within constants, and one-shot gossip is solved within polylog factors in every graph.